In the rest of this section we focus on left nilpotency. In [1]} a family of left nilpotent left semi-braces was exhibited. In particular, they provided left nilpotent left semi-braces having nilpotent multiplicative group and with \(E\)  contained in the centralizer of \(G\)  or such that is a normal subgroup of \((B,\circ )\) . Below, we show sufficient conditions for the left semi-braces of teostrutt which ensure left nilpotency.
